{% extends "homepage.html" %}

{% block content %}

<p>

      <h2>Browse {{KNOWL('lf', title="local number fields")}}</h2>
<p>

The table gives for each $p$ and $n$ shown, the number of degree $n$ extensions
of $\mathbb{Q}_p$ up to isomorphism.
<p>
<table border=1 cellpadding=5 class='right_align_table'>
<tr>
<th>$p$ \ $n$</th>
<th>2</th> <th>3</th> <th>4</th> <th>5</th> <th>6</th>
<th>7</th> <th>8</th> <th>9</th> <th>10</th> <th>11</th>
</tr>
<tr>
<th>2</th> <td><a href="?p=2&n=2">7</a></td> <td><a href="?p=2&n=3">2</a></td> <td><a href="?p=2&n=4">59</a></td> <td><a href="?p=2&n=5">2</a></td> <td><a href="?p=2&n=6">47</a></td> <td><a href="?p=2&n=7">2</a></td> <td><a href="?p=2&n=8">1823</a></td> <td><a href="?p=2&n=9">3</a></td> <td><a href="?p=2&n=10">158</a></td> <td><a href="?p=2&n=11">2</a></td>
</tr>
<tr>
<th>3</th>
<td><a href="?p=3&n=2">3</a></td> <td><a href="?p=3&n=3">10</a></td> <td><a href="?p=3&n=4">5</a></td> <td><a href="?p=3&n=5">2</a></td> <td><a href="?p=3&n=6">75</a></td> <td><a href="?p=3&n=7">2</a></td> <td><a href="?p=3&n=8">8</a></td> <td><a href="?p=3&n=9">795</a></td> <td><a href="?p=3&n=10">6</a></td> <td><a href="?p=3&n=11">2</a></td>
</tr>
<tr>
<th>5</th>
<td><a href="?p=5&n=2">3</a></td> <td><a href="?p=5&n=3">2</a></td> <td><a href="?p=5&n=4">7</a></td> <td><a href="?p=5&n=5">26</a></td> <td><a href="?p=5&n=6">7</a></td> <td><a href="?p=5&n=7">2</a></td> <td><a href="?p=5&n=8">11</a></td> <td><a href="?p=5&n=9">3</a></td> <td><a href="?p=5&n=10">258</a></td> <td><a href="?p=5&n=11">2</a></td>
</tr>
<tr>
<th>7</th>
<td><a href="?p=7&n=2">3</a></td> <td><a href="?p=7&n=3">4</a></td> <td><a href="?p=7&n=4">5</a></td> <td><a href="?p=7&n=5">2</a></td> <td><a href="?p=7&n=6">12</a></td> <td><a href="?p=7&n=7">50</a></td> <td><a href="?p=7&n=8">8</a></td> <td><a href="?p=7&n=9">7</a></td> <td><a href="?p=7&n=10">6</a></td> <td><a href="?p=7&n=11">2</a></td> 
</tr>
<tr>
<th>11</th>
<td><a href="?p=11&n=2">3</a></td> <td><a href="?p=11&n=3">2</a></td> <td><a href="?p=11&n=4">5</a></td> <td><a href="?p=11&n=5">6</a></td> <td><a href="?p=11&n=6">7</a></td> <td><a href="?p=11&n=7">2</a></td> <td><a href="?p=11&n=8">8</a></td> <td><a href="?p=11&n=9">3</a></td> <td><a href="?p=11&n=10">18</a></td> <td><a href="?p=11&n=11">122</a></td> 
</tr>
<tr>
<th>13</th>
<td><a href="?p=13&n=2">3</a></td> <td><a href="?p=13&n=3">4</a></td> <td><a href="?p=13&n=4">7</a></td> <td><a href="?p=13&n=5">2</a></td> <td><a href="?p=13&n=6">12</a></td> <td><a href="?p=13&n=7">2</a></td> <td><a href="?p=13&n=8">11</a></td> <td><a href="?p=13&n=9">7</a></td> <td><a href="?p=13&n=10">6</a></td> <td><a href="?p=13&n=11">2</a></td>
</tr>
<tr>
<th>17</th>
<td><a href="?p=17&n=2">3</a></td> <td><a href="?p=17&n=3">2</a></td> <td><a href="?p=17&n=4">7</a></td> <td><a href="?p=17&n=5">2</a></td> <td><a href="?p=17&n=6">7</a></td> <td><a href="?p=17&n=7">2</a></td> <td><a href="?p=17&n=8">15</a></td> <td><a href="?p=17&n=9">3</a></td> <td><a href="?p=17&n=10">6</a></td> <td><a href="?p=17&n=11">2</a></td>
</tr>
<tr>
<th>19</th>
<td><a href="?p=19&n=2">3</a></td> <td><a href="?p=19&n=3">4</a></td> <td><a href="?p=19&n=4">5</a></td> <td><a href="?p=19&n=5">2</a></td> <td><a href="?p=19&n=6">12</a></td> <td><a href="?p=19&n=7">2</a></td> <td><a href="?p=19&n=8">8</a></td> <td><a href="?p=19&n=9">13</a></td> <td><a href="?p=19&n=10">8</a></td> <td><a href="?p=19&n=11">2</a></td>
</tr>
<tr>
<th>23</th>
<td><a href="?p=23&n=2">3</a></td> <td><a href="?p=23&n=3">2</a></td> <td><a href="?p=23&n=4">5</a></td> <td><a href="?p=23&n=5">2</a></td> <td><a href="?p=23&n=6">7</a></td> <td><a href="?p=23&n=7">2</a></td> <td><a href="?p=23&n=8">8</a></td> <td><a href="?p=23&n=9">3</a></td> <td><a href="?p=23&n=10">6</a></td> <td><a href="?p=23&n=11">12</a></td> 
</tr>

</table>
<p>

    <h2>Find a specific local number field</h2>

    <form name="search" method = "get" action="{{search}}">      
	  Search by {{KNOWL('lf.field.label',title="label")}}
          <input type="text" name="jump_to" value="" placeholder="2.4.6.7"> 
          <input type="submit" value="Find">
        </form>
    </td>
</tr>

        <h2>Search</h2>
      <form name="search" method = "get" action="{{search}}">
        <table class="">
          <tr>
            <td>
          {{KNOWL('lf.degree',title='Degree')}}:
            </td><td><input type="text" name="n" value="" example="6"></td>
          </tr>
          <tr>
            <td>
              Prime $p$ for base field  {{KNOWL('lf.qp',title='$\mathbb{Q}_p$')}}:
            </td><td><input type="text" name="p" value="" example="3"></td>
          </tr>
          <tr>
            <td>
              {{KNOWL('lf.discriminant_exponent',title='Discriminant
              exponent')}} $c$:
            </td><td><input type="text" name="c" value="" example="8"></td>
          </tr>
          <tr>
            <td>
              {{KNOWL('lf.ramification_index',title='Ramification
              index')}} $e$:
            </td><td><input type="text" name="e" value="" example="3"></td>
          </tr>
<!--      
          <tr>
          <td>
              Maximum number of fields to display:
            </td><td><input type="text" name="count" value="25"></td>
          </tr>
-->
  </table>
        <input type="submit" name="Submit" value="Search">
      </form>



{% endblock %}
